Hidden attractors in fundamental problems and engineering models

TL;DR

This paper discusses the concept of hidden attractors in dynamical systems, highlighting their distinction from self-excited attractors and exploring methods to identify and analyze them in various models.

Contribution

It provides a comprehensive survey of hidden and self-excited attractors, clarifying their definitions, significance, and the challenges in predicting hidden attractors in systems.

Findings

Hidden attractors exist in systems with no or one stable equilibrium.

Standard methods can find self-excited attractors but not hidden ones.

The paper offers examples illustrating the differences between attractor types.

Abstract

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered.